Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression

Waldmann, Elisabeth; Kneib, Thomas

doi:10.1007/s11222-014-9480-2

Cited by 4 publications

(4 citation statements)

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“…We applied four different specification/estimation methods: FE refers to the fixed effects panel quantile regression (Koenker ) with optimal shrinkage estimated following Lamarche (); CRE is the correlated random effects estimator of Abrevaya and Dahl () amended following Bache et al () to allow for unbalanced panels; MCMC is a Bayesian formulation with country random effects with Dirichlet process priors, estimated by the modified Markov Chain Monte Carlo algorithm of Waldmann et al (). This version has been chosen because of improved convergence; VA is a computational simplification of the Bayesian formulation with more restrictive Gaussian priors on the random effects and estimated using the variational approximation method of Waldmann and Kneib (). This provides a more restrictive model, but considerably reduces the computational costs. …”

Section: Resultsmentioning

confidence: 99%

“…Although by far the most popular, the Koenker () estimator is the most demanding computationally in that the search for optimal amount of shrinkage carries considerable computational costs. Bayesian estimation via Markov Chain Monte Carlo (MCMC) simulation is always computationally demanding, but workable approximations, such as variational inference (Waldmann and Kneib ), or (integrated nested) Laplace approximation (Yue and Rue ) are available to reduce the computational costs. Finally, the CRE approach is computationally the most appealing, although it requires practical examination and justification of the identification assumptions and hence may not always be applicable to the specific estimation problem.…”

Section: Methodsmentioning

confidence: 99%

“…With regard to the random effect formulation, we have implemented Bayesian MCMC inference using the sampling scheme suggested in Waldmann et al () which avoids the mixing and convergence issues found by Yue and Rue (). We have implemented the variational approximation as detailed in Waldmann and Kneib ().…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Convergence: A Story of Quantiles and Spillovers

Kostov¹,

Gallo

2015

Kyklos

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Summary In this paper, we revisit the analysis of cross‐country convergence by combining spatial econometrics and panel quantile regressions to estimate conditional β‐convergence models. Moreover, we use both exogenous and endogenous weight matrices. Our results show that indeed the effects of initial per capita income, investment rate, population growth and human capital on growth rates vary considerably across the estimated quantiles. Convergence is not a generalized phenomenon across the conditional growth distribution. Moreover, while using exogenous spatial weight matrices does not substantially alter the findings found in a‐spatial models, it appears that endogenous weights dramatically affect the estimates of the convergence process.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Convergence: A Story of Quantiles and Spillovers

Kostov¹,

Gallo

2015

Kyklos

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“…Under the topic of other inferential approaches, I would particularly be interested in hearing Simon's opinion on the ability of variational approximations for estimating complex generalized additive models. Waldmann and Kneib (2015) have utilized these for inference in Gaussian mean regression and quantile regression (again based on the working likelihood of the asymmetric Laplace distribution) where similar schemes as with Gibbs sampling in Markov chain Monte Carlo simulations can be derived. On the other hand, they also found that uncertainty quantification tends to be complicated using simple forms of variational approximations.…”

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confidence: 99%

Comments on: Inference and computation with Generalized Additive Models and their extensions

Kneib

2020

TEST

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It is my pleasure to contribute to the discussion of Simon's paper on "Inference and computation with Generalized Additive Models and their extensions" which provides an excellent overview of the current state of the art of the class of Generalized Additive Models in a broad sense, i.e., including several modern developments such as functional effects, interaction surfaces or distributional regression. I particularly enjoyed the brief yet very informative summaries of inferential results and statistical computing where Simon takes a delightful pragmatic perspective by focusing on the applied and computational pros and cons of approaches such as penalized likelihood, Markov chain Monte Carlo simulations, integrated nested Laplace approximations or functional gradient descent boosting. I believe that such a pragmatic perspective is indeed required to bring recent advances concerning statistical modeling to applied scientists utilizing these modeling techniques.Another necessity for the future success of extended generalized additive models, from my perspective, is considerably more work focusing on interpretation, visualization or uncertainty quantification for such models if these should be routinely used by applied researchers. In fact, already simple generalized linear models pose considerable challenges concerning interpretation. While in some cases ceteris paribus-type interpretations are still conceivable, these are usually restricted either to transformations of the expectation of the response (e.g., log odds in logistic regression or log expectations in Poisson regression) or to relative effects (e.g., on odds in logistic regression or the expectation in Poisson regression). While such relations are certainly relevant and can be interpreted correctly with enough care, they can also easily lead to misleading conclusions. For example, a significant multiplicative and therefore relative effect on the odds in logistic regression does not necessarily lead to a relevant effect on the actual probability for observing the event of interest, depending, for example, on the value of the intercept or the values of the other covariates consid-This comment refers to the invited paper available at: https://doi.

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A variational inference for the Lévy adaptive regression with multiple kernels

Lee

2022

Comput Stat

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Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression

Cited by 4 publications

References 20 publications

Convergence: A Story of Quantiles and Spillovers

Convergence: A Story of Quantiles and Spillovers

Comments on: Inference and computation with Generalized Additive Models and their extensions

A variational inference for the Lévy adaptive regression with multiple kernels

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